The Colors of Noise

Talking about the ‘science’ of something often evokes ideas like precision, or a very controlled study where every parameter is meticulously accounted for. But the natural world is not necessarily precise or controlled; evolution gives the quickest functional solution, rather than the most elegant. And as with entropy, management of disorder and messiness is often simpler to achieve than full control. So even as we attempt to study and engineer our natural environment, we have to accept some level of randomness and chaos, or even perhaps take advantage of it as nature does.

It’s with that in mind that I’d like to talk about noise. Colloquially, noise refers to sounds, but specifically disordered or cacophonous ones. This comes from the idea of noise as a sort of randomness that’s part of a signal carrying information, like static on a phone line or a video. Those examples of noise are like random factors that affect the timbre or perception of the signal itself, but one can also think about noise more generally in nature as a perceivable, measurable result of some inherently random physical process. Such processes are called ‘stochastic’, as opposed to ‘deterministic’ processes where the probability is determined or fixed by the initial conditions.

But as you might imagine, there are lots of different physical phenomena that might lead to noise. So the noise resulting from stochastic processes has a sort of fingerprint that can be read out and may give useful information about the system the noise came from. For example, noise on a telephone line may be different from noise in a photodetector, even if both come from random things that electrons are doing in the material. But how to tell the two apart? Variations in noise are usually analysed by separating out the noise by frequency, which is to say looking at what parts of the signal occur once per second, versus twice per second, versus a hundred or a thousand times per second. This is described as the ‘power spectrum’ of the noise, but more lyrically, the most common power spectra for naturally occurring noise are called the colors of noise.

The power spectrum above shows noise that has the same power at all frequencies, which is called white noise, because of the idea that white light contains all the visible colors in equal proportions. White noise comes from thermal processes, which is to say atoms using the heat and kinetic energy around them to jump up to higher energy states and then back down. And since thermal processes don’t have any preference for one frequency of activity over another, the frequency spread of thermal noise is flat.

There’s also brown noise, which isn’t named for the color brown but rather for the scientist Robert Brown. He was a botanist who discovered that pollen grains in water moved in a random pattern when observed under a microscope, and initially could not explain the mechanism. Many decades later, Einstein explained the movement as a result of molecules in the water buffeting the pollen grains, causing a random movement of the grain itself to be visible even though the water molecules were too small to see. This movement is called Brownian motion, or a random walk, and so Brownian noise is characterized by enhanced low frequencies as you’d get in a random walk. Auditory brown noise sounds like a waterfall, softer than the other colors of noise. Here’s an animation of the pollen grains colliding with smaller water molecules, where you can see the randomness that we can call noise:

Pink noise, or flicker noise, decreases in power as the frequency of the noise increases. It’s also called 1/f noise, because the power of pink noise goes inversely as the frequency f. Pink noise comes from the trapping and detrapping of charge carriers like electrons, which can be counted as a stochastic process that is more likely at lower frequencies. Because the human ear is less sensitive to higher frequency noises, pink noise is often used as a reference signal in audio engineering.

But just as with light, our senses and processing of noise can distort it between its physical origin and our perception of it. So for example, we may perceive white noise, which has a flat power spectrum, as louder for frequencies that our ear can better detect. I mentioned before that the human ear is less sensitive to higher frequencies, but overall that sensitivity can be mapped to create a power spectrum that will appear flat given our sensory distortion. This sort of noise is called grey noise.

There are other colors of noise, such and blue and violet noise which increase in power at higher frequencies, green noise which is the selected center of the power spectrum for white noise, and black noise which is a fancy way of saying silence. You can listen to some colors of noise here. There is also a type of noise specific to small numbers of some countable event like trapping and detrapping, where the discreteness of the event becomes important. Fluctuations in a small number matter more than fluctuations in a large number. This is called shot noise, and is common in any signal that has a small number of countable events, like measuring individual electrons or photons. But noise is just a consequence of the inherent randomness in our physical world, an avatar revealing the exact physical mechanism behind its own creation.

3 responses to “The Colors of Noise”

Very nicely done. Thank you.
You listed two of our senses, sight and hearing, in which noise is important. Is there important information contained in the noise inherent in our other senses — smell, taste, and touch? It would seem, from an evolutionary perspective, that noise would be important in these senses as well. What might be the color of noise in detecting the smell of a lilac?

Well, there would definitely be some amount of brown noise inherent in any of those detection systems, just due to thermal processes and the molecular detection mechanisms. But also, less than a year ago, some scientists attempted to make an olfactory white:

Interesting link.
I wonder if, in the presence of white smell, people are still very sensitized to rare but important smells such as the smell of predator or fear. for instance the smell of a tiger in a jungle of flowers. It seems that humans and other animals have to respond quickly and accurately to critical smells even in the presence of white smell. Do people respond quickly to low level patterned distortions in white noise or white light when the distortions contain an ‘important’ signal?